Proposition 2.4 [1]}
Let \(U\)  be an open interval and \(f:U \rightarrow \mathbb {R}\)  an analytic function.
If there exists a convergent sequence \((x_n)_{n \in \mathbb {N}}\)  in \(U\)  where \(f(x_n)=0\)  for all \(n \in \mathbb {N}\)  and \(\lim _{n \rightarrow \infty } x_n \in U\) ,
then \(Z(f)=U\) .

